Generally, a gain drift of a VCO in a PLL may be generated due to some uncontrolled factors, e.g., variations of a manufacturing process, changes of an ambient temperature and changes of a power source, such that the PLL cannot remain at a predetermined close loop bandwidth in practical applications. More particularly, when an offset PLL is applied to a signal transmitting end of a wireless communication system, e.g., a transmitter of a Global System for Mobile Communication (GSM) system, a data signal is directly converted into a radio frequency (RF) signal, then the RF signal transmitted by a power amplifier. However, since the offset PLL transmitter comprises an intermediate frequency (IF) mixer for up-converting the transmitted data signal into an IF signal, the IF mixer also produces bandwidth noises. At this point, the offset PLL transmitter needs to remove the bandwidth noises produced by the IF mixer via a close-loop bandwidth. However, the close loop bandwidth of the offset PLL is undesirably affected by uncontrolled factors, e.g., variations of a manufacturing process variations, changes of an ambient temperature, and changes of a power source voltage, such that the close loop bandwidth cannot remain at a predetermined close-loop bandwidth. Therefore, a problem of calibrating the close loop bandwidth of the offset PLL to remain at the predetermined close loop bandwidth needs to be solved.